Stability analysis for interconnected systems with “mixed” passivity, negative-imaginary and small-gain properties

An analytical framework to examine the finite-gain stability for a positive feedback interconnection between two stable, linear time-invariant systems where one system has “mixed” passivity, negative-imaginary and small-gain properties and the other system has “mixed” negative-imaginary, negative-passivity, and small-gain properties is proposed. A classical Nyquist argument is used to examine the stability of the interconnected systems and the usefulness of the proposed framework is illustrated by a numerical example.